Standard atmosphere - University of Utahhome.chpc.utah.edu/~u0035056/oldclass/3000/Lecture...Nov 02,...
Transcript of Standard atmosphere - University of Utahhome.chpc.utah.edu/~u0035056/oldclass/3000/Lecture...Nov 02,...
Standard atmosphereStandard atmospherePressure (mb)
Typical height (ft)
Typical height (m)
1013.25 0 01000 370 110850 4780 1460700 9880 3010500 18280 5570300 30050 9160
Whiteman 2000
Pressure decreases exponentially with altitude
Horizontal Variations in PressureHorizontal Variations in Pressure• Pressure changes more rapidly in the
vertical than in the horizontal • Vertically: 1000-850 mb in 1500 m
• Horizontally: order 10 mb in 1000 km
• Horizontal pressure gradient force is weaker than vertical pressure gradient force
• Environment tends to be in hydrostatic balance with very small motion in the vertical (vertical pressure gradient force balanced by gravity)
Horizontal Wind AccelerationsHorizontal Wind Accelerations• Horizontal accelerations in wind are due to
imbalance between: • horizontal variations in mass (pressure)
• non-inertial (Coriolis) force due to rotation of earth
• frictional effects (near the surface)
Choice of Vertical CoordinateChoice of Vertical Coordinate• Use height as vertical
coordinate?• How does pressure
vary horizontally on a surface of constant height? – Sea level pressure
“map”– 1500 m pressure “map”– Contour values of equal
pressure (isobars)– Force due to inequitable
distribution of mass defined by pressure gradient force
Sea level pressure analysis
Sea Level PressureSea Level Pressure
Choice of Vertical CoordinateChoice of Vertical Coordinate• Use pressure as a
vertical coordinate?• How does height vary
horizontally on a surface of constant pressure?– 1000 mb height “map”– 500 mb height “map”– Contour values of equal
height (isoheights)– Force due to inequitable
distribution of mass defined by height gradient force
500 mb Height analysis
Ridges/Troughs in the TroposphereRidges/Troughs in the Troposphere
Whiteman (2000)
Height Gradient ForceHeight Gradient Force
5520 m
5640 m
120 min 500 km
120 min 1000 km
H
L
Directed from High Height to Low HeightDirected from High Height to Low HeightMagnitude proportional to distance between Magnitude proportional to distance between isoheightsisoheights
H
H
Frictional ForceFrictional Force
5520 m
5640 m
Directed behind windDirected behind windMagnitude proportional to wind speedMagnitude proportional to wind speed
H
HH
L
CoriolisCoriolis ForceForce
5520 m
5640 m
Arises due to rotation of earthArises due to rotation of earthDirected perpendicular to wind (to right in NH)Directed perpendicular to wind (to right in NH)Magnitude proportional to latitude and wind speedMagnitude proportional to latitude and wind speed
H
HH
L
GeostrophicGeostrophic BalanceBalance• Ignore friction for the moment
• Distribution of mass evolves in space and time
• Wind speed and direction tends to adjust in order to maintain balance between pressure (height) gradient and Coriolis forces• For example, if pressure (height) gradient increases locally, wind
speed increases locally to compensate
• Even as the mass field changes, we can define the geostrophicwind Vg as the wind that is in balance with the pressure (height) gradient force at each instant
• So Vg varies in time and space as the mass field changes in time and space
GeostrophicGeostrophic Wind VWind Vgg
5520 m
5640 m
Directed parallel to pressure (height) contoursDirected parallel to pressure (height) contoursLow height (pressure) to the left of the windLow height (pressure) to the left of the windMagnitude proportional to pressure (height) gradientMagnitude proportional to pressure (height) gradient
H
HH
L
VgVg
Vg
BuysBuys--Ballot rule (Northern Ballot rule (Northern Hemisphere)Hemisphere)
“If the wind blows into your back, the Low will be to your Left (and the high will be to your right).”
This rule works well if the wind is above the earth’s boundary layer, not channeled by topography, etc.
January Mean HeightJanuary Mean Height
Whiteman (2000)
AgeostrophicAgeostrophic WindWind
• To zeroth order the actual wind V tends to be close to the geostrophic wind in the free atmosphere
• The difference between the actual wind V and the geostrophic wind Vg is the ageostrophic (nongeostrophic) wind
• Ageostrophic wind is large when– Friction is important– Height contours are strongly curved
AgeostrophicAgeostrophic Wind Wind VVaa
5520 m
5640 m
••If friction important, balanced wind will have componentIf friction important, balanced wind will have componentdirected towards low height (pressure)directed towards low height (pressure)••Balanced wind V will be weaker in magnitude than Balanced wind V will be weaker in magnitude than geostrophicgeostrophicwindwind
H
L
H
H
Vg
Vg
VgV
Va
V
V
PlanetaryPlanetary--Scale Mountain WavesScale Mountain Waves
• Planetary-scale waves are observed that remain fixed with respect to the earth’s surface:
• Possible causes are geographic distribution of:– Mountains (Charney and Eliassen 1949)– Land/sea differences and inequitable distribution of
sensible and latent heating (Smagorinsky 1953)• After 30 years of debate, answer settled that
both are important, but mountains perhaps a little more so
GrossGross--simplification of planetarysimplification of planetary--scale scale stationary wavesstationary waves
Himalayas/Tibetan Plateau
Rockies
Upper-troposphericflow
Kur
oshi
o
Gul
f Stre
am
January Mean HeightJanuary Mean Height
Whiteman (2000)
Jet StreamJet Stream
Whiteman (2000)
CyclogenesisCyclogenesis
• The formation of intensification of low pressure systems (cyclones)
• Often occurs in the lee of major mountain barriers
Areas of Areas of CyclogenesisCyclogenesis
Whiteman (2000)
AnticyclogenesisAnticyclogenesis
• Formation or intensification of a high pressure system (anticyclone)
Areas of Areas of AnticyclogenesisAnticyclogenesis
Whiteman (2000)
Conservation of Potential Conservation of Potential VorticityVorticity
• Quantities that are conserved (unchanging) are good tracers
• Potential vorticity tends to be conserved for large scale motions in the atmosphere
• PV = rotation/depth of fluid• PV = η/p = (ζ+f)/p
η = (ζ+f) = absolute vorticityζ = relative vorticity: local rotation about vertical axis. Cyclones have positive spin in NH
• f = planetary vorticity: spin due to rotation of earth about its axis. Earth has positive spin in NH
Potential VorticityPotential Vorticity• If the depth of the fluid decreases, then the absolute
vorticity must decrease
• Parcel must acquire anticyclonic absolute vorticity • A parcel with an initial cyclonic rotation could decrease ζ
(cyclonic rotation weakens or becomes anticyclonic), decreasing f (parcel moves equatorward), or both
(ζ+f)0 >0
Depth decreases ?(ζ +f)f < (ζ +f)0
pp
• If the depth of the fluid increases, then the absolute vorticity must increase
• Parcel must acquire cyclonic absolute vorticity • A parcel with an initial cyclonic rotation could
increase ζ (cyclonic rotation strengthens), increase f (parcel moves poleward), or both
p
Potential VorticityPotential Vorticity
(ζ +f)f > (ζ +f)0
Depth increases
(ζ +f)0 > 0
p
How can we make or strengthen a cyclone?How can we make or strengthen a cyclone?• Need to increase low-level cyclonic vorticity• Must stretch low-level fluid columns• To stretch the column, we need middle-tropospheric
ascent, near-surface descent, or both
(ζ +f)f > (ζ +f)0
Column stretches
(ζ +f)0 > 0
pp
Development of Lee Side TroughDevelopment of Lee Side Trough
Column stretches
(η+f) increases
Column compresses
(η+f) decreases
Column stretches
(η+f) increases
Column compresses
(η+f) decreases
z
x
y
xWindward
RidgeLee
TroughWaveTrain